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146 Living Energies Applied to the concepts of Kepler, who was the first person to determine that the orbits of the planets were eccentric about the Sun, this same equation opens up a plethora of interest- ing insights in its three-dimensional form, namely as the hyperbolic cone shown in fig. 11.5. When he first put pen to paper, Kepler initially described the planetary orbits as oval, i.e. egg-shaped (ovum=egg), but because he was unable to define them mathe- matically, he was eventually forced to adopt the simpler ellipse, which for most of the plan- etary orbits is a fairly close approximation. Whereas an elliptical orbit has two foci - the Sun occupying one, the other being empty - and a symmetry about both axes, an egg-orbit has but one focus - the unequivocal and only possible location for the Sun - and is symmet- rical about the longitudinal axis only. In comparison with the thoroughly sym- metrical ellipse, the constantly changing cur- vature of the egg-orbit far better reflects the varying strength of the Sun's gravitational attraction as the planet moves around it. Moreover the egg's dissimilar curvature at opposite ends likewise far better reflects the varying speed and the resultant path followed by the planet as it accelerates towards the Sun, until it reaches its maximum orbital velocity at perihelion (position closest to the Sun; blunt end of the egg). Having passed this point the planet then decelerates, attaining its minimum velocity at aphelion (position furthest from the Sun; sharp end of the egg). Both terms, perihe- lion and aphelion, are of Kepler's coinage. By taking a section through this solid a cone at a steeply inclined plane, the resultant flatPDF Image | Viktor Schauberger Work Explained
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